LMFDB - Embedded newform 8013.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80990 q^{2} +1.00000 q^{3} +5.89553 q^{4} +3.04419 q^{5} -2.80990 q^{6} +3.35815 q^{7} -10.9460 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.80990 q^{2} +1.00000 q^{3} +5.89553 q^{4} +3.04419 q^{5} -2.80990 q^{6} +3.35815 q^{7} -10.9460 q^{8} +1.00000 q^{9} -8.55386 q^{10} +3.20260 q^{11} +5.89553 q^{12} +6.42536 q^{13} -9.43606 q^{14} +3.04419 q^{15} +18.9662 q^{16} -6.70387 q^{17} -2.80990 q^{18} +5.19441 q^{19} +17.9471 q^{20} +3.35815 q^{21} -8.99897 q^{22} -1.38780 q^{23} -10.9460 q^{24} +4.26709 q^{25} -18.0546 q^{26} +1.00000 q^{27} +19.7981 q^{28} +5.04354 q^{29} -8.55386 q^{30} -9.32809 q^{31} -31.4010 q^{32} +3.20260 q^{33} +18.8372 q^{34} +10.2228 q^{35} +5.89553 q^{36} +1.94322 q^{37} -14.5958 q^{38} +6.42536 q^{39} -33.3218 q^{40} -8.32135 q^{41} -9.43606 q^{42} +7.92471 q^{43} +18.8810 q^{44} +3.04419 q^{45} +3.89957 q^{46} +3.46968 q^{47} +18.9662 q^{48} +4.27717 q^{49} -11.9901 q^{50} -6.70387 q^{51} +37.8809 q^{52} +0.587042 q^{53} -2.80990 q^{54} +9.74931 q^{55} -36.7584 q^{56} +5.19441 q^{57} -14.1718 q^{58} +1.13952 q^{59} +17.9471 q^{60} +0.747596 q^{61} +26.2110 q^{62} +3.35815 q^{63} +50.3013 q^{64} +19.5600 q^{65} -8.99897 q^{66} +6.42956 q^{67} -39.5228 q^{68} -1.38780 q^{69} -28.7252 q^{70} -7.60177 q^{71} -10.9460 q^{72} -11.8116 q^{73} -5.46025 q^{74} +4.26709 q^{75} +30.6238 q^{76} +10.7548 q^{77} -18.0546 q^{78} -16.7142 q^{79} +57.7367 q^{80} +1.00000 q^{81} +23.3821 q^{82} +8.13069 q^{83} +19.7981 q^{84} -20.4078 q^{85} -22.2676 q^{86} +5.04354 q^{87} -35.0558 q^{88} +8.78685 q^{89} -8.55386 q^{90} +21.5773 q^{91} -8.18180 q^{92} -9.32809 q^{93} -9.74945 q^{94} +15.8128 q^{95} -31.4010 q^{96} -5.64165 q^{97} -12.0184 q^{98} +3.20260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.80990	−1.98690	−0.993449	−	0.114275i	$-0.963545\pi$
$2$	−2.80990	−1.98690	−0.993449	+	0.114275i	$0.963545\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.89553	2.94776
$5$	3.04419	1.36140	0.680701	−	0.732561i	$-0.261675\pi$
$5$	3.04419	1.36140	0.680701	+	0.732561i	$0.261675\pi$
$6$	−2.80990	−1.14714
$7$	3.35815	1.26926	0.634631	−	0.772816i	$-0.281152\pi$
$7$	3.35815	1.26926	0.634631	+	0.772816i	$0.281152\pi$
$8$	−10.9460	−3.87001
$9$	1.00000	0.333333
$10$	−8.55386	−2.70497
$11$	3.20260	0.965620	0.482810	−	0.875725i	$-0.339616\pi$
$11$	3.20260	0.965620	0.482810	+	0.875725i	$0.339616\pi$
$12$	5.89553	1.70189
$13$	6.42536	1.78207	0.891037	−	0.453931i	$-0.149979\pi$
$13$	6.42536	1.78207	0.891037	+	0.453931i	$0.149979\pi$
$14$	−9.43606	−2.52189
$15$	3.04419	0.786006
$16$	18.9662	4.74155
$17$	−6.70387	−1.62593	−0.812963	−	0.582315i	$-0.802147\pi$
$17$	−6.70387	−1.62593	−0.812963	+	0.582315i	$0.802147\pi$
$18$	−2.80990	−0.662299
$19$	5.19441	1.19168	0.595840	−	0.803103i	$-0.296819\pi$
$19$	5.19441	1.19168	0.595840	+	0.803103i	$0.296819\pi$
$20$	17.9471	4.01310
$21$	3.35815	0.732808
$22$	−8.99897	−1.91859
$23$	−1.38780	−0.289376	−0.144688	−	0.989477i	$-0.546218\pi$
$23$	−1.38780	−0.289376	−0.144688	+	0.989477i	$0.546218\pi$
$24$	−10.9460	−2.23435
$25$	4.26709	0.853418
$26$	−18.0546	−3.54080
$27$	1.00000	0.192450
$28$	19.7981	3.74148
$29$	5.04354	0.936562	0.468281	−	0.883580i	$-0.344874\pi$
$29$	5.04354	0.936562	0.468281	+	0.883580i	$0.344874\pi$
$30$	−8.55386	−1.56171
$31$	−9.32809	−1.67537	−0.837687	−	0.546151i	$-0.816093\pi$
$31$	−9.32809	−1.67537	−0.837687	+	0.546151i	$0.816093\pi$
$32$	−31.4010	−5.55097
$33$	3.20260	0.557501
$34$	18.8372	3.23055
$35$	10.2228	1.72798
$36$	5.89553	0.982588
$37$	1.94322	0.319464	0.159732	−	0.987160i	$-0.448937\pi$
$37$	1.94322	0.319464	0.159732	+	0.987160i	$0.448937\pi$
$38$	−14.5958	−2.36775
$39$	6.42536	1.02888
$40$	−33.3218	−5.26864
$41$	−8.32135	−1.29958	−0.649788	−	0.760116i	$-0.725142\pi$
$41$	−8.32135	−1.29958	−0.649788	+	0.760116i	$0.725142\pi$
$42$	−9.43606	−1.45602
$43$	7.92471	1.20851	0.604253	−	0.796792i	$-0.293471\pi$
$43$	7.92471	1.20851	0.604253	+	0.796792i	$0.293471\pi$
$44$	18.8810	2.84642
$45$	3.04419	0.453801
$46$	3.89957	0.574960
$47$	3.46968	0.506105	0.253053	−	0.967453i	$-0.418565\pi$
$47$	3.46968	0.506105	0.253053	+	0.967453i	$0.418565\pi$
$48$	18.9662	2.73754
$49$	4.27717	0.611024
$50$	−11.9901	−1.69565
$51$	−6.70387	−0.938729
$52$	37.8809	5.25313
$53$	0.587042	0.0806364	0.0403182	−	0.999187i	$-0.487163\pi$
$53$	0.587042	0.0806364	0.0403182	+	0.999187i	$0.487163\pi$
$54$	−2.80990	−0.382379
$55$	9.74931	1.31460
$56$	−36.7584	−4.91205
$57$	5.19441	0.688017
$58$	−14.1718	−1.86085
$59$	1.13952	0.148353	0.0741764	−	0.997245i	$-0.476367\pi$
$59$	1.13952	0.148353	0.0741764	+	0.997245i	$0.476367\pi$
$60$	17.9471	2.31696
$61$	0.747596	0.0957198	0.0478599	−	0.998854i	$-0.484760\pi$
$61$	0.747596	0.0957198	0.0478599	+	0.998854i	$0.484760\pi$
$62$	26.2110	3.32880
$63$	3.35815	0.423087
$64$	50.3013	6.28766
$65$	19.5600	2.42612
$66$	−8.99897	−1.10770
$67$	6.42956	0.785496	0.392748	−	0.919646i	$-0.371524\pi$
$67$	6.42956	0.785496	0.392748	+	0.919646i	$0.371524\pi$
$68$	−39.5228	−4.79285
$69$	−1.38780	−0.167071
$70$	−28.7252	−3.43331
$71$	−7.60177	−0.902164	−0.451082	−	0.892483i	$-0.648962\pi$
$71$	−7.60177	−0.902164	−0.451082	+	0.892483i	$0.648962\pi$
$72$	−10.9460	−1.29000
$73$	−11.8116	−1.38244	−0.691221	−	0.722643i	$-0.742927\pi$
$73$	−11.8116	−1.38244	−0.691221	+	0.722643i	$0.742927\pi$
$74$	−5.46025	−0.634742
$75$	4.26709	0.492721
$76$	30.6238	3.51279
$77$	10.7548	1.22562
$78$	−18.0546	−2.04428
$79$	−16.7142	−1.88049	−0.940247	−	0.340494i	$-0.889406\pi$
$79$	−16.7142	−1.88049	−0.940247	+	0.340494i	$0.889406\pi$
$80$	57.7367	6.45516
$81$	1.00000	0.111111
$82$	23.3821	2.58213
$83$	8.13069	0.892459	0.446229	−	0.894919i	$-0.352767\pi$
$83$	8.13069	0.892459	0.446229	+	0.894919i	$0.352767\pi$
$84$	19.7981	2.16015
$85$	−20.4078	−2.21354
$86$	−22.2676	−2.40118
$87$	5.04354	0.540724
$88$	−35.0558	−3.73696
$89$	8.78685	0.931404	0.465702	−	0.884942i	$-0.345802\pi$
$89$	8.78685	0.931404	0.465702	+	0.884942i	$0.345802\pi$
$90$	−8.55386	−0.901656
$91$	21.5773	2.26192
$92$	−8.18180	−0.853012
$93$	−9.32809	−0.967278
$94$	−9.74945	−1.00558
$95$	15.8128	1.62236
$96$	−31.4010	−3.20485
$97$	−5.64165	−0.572822	−0.286411	−	0.958107i	$-0.592462\pi$
$97$	−5.64165	−0.572822	−0.286411	+	0.958107i	$0.592462\pi$
$98$	−12.0184	−1.21404
$99$	3.20260	0.321873
$100$	25.1567	2.51567
$101$	9.71049	0.966229	0.483115	−	0.875557i	$-0.339505\pi$
$101$	9.71049	0.966229	0.483115	+	0.875557i	$0.339505\pi$
$102$	18.8372	1.86516
$103$	−12.4125	−1.22304	−0.611519	−	0.791229i	$-0.709441\pi$
$103$	−12.4125	−1.22304	−0.611519	+	0.791229i	$0.709441\pi$
$104$	−70.3322	−6.89664
$105$	10.2228	0.997647
$106$	−1.64953	−0.160216
$107$	13.5602	1.31092	0.655459	−	0.755231i	$-0.272475\pi$
$107$	13.5602	1.31092	0.655459	+	0.755231i	$0.272475\pi$
$108$	5.89553	0.567298
$109$	−1.33687	−0.128049	−0.0640244	−	0.997948i	$-0.520394\pi$
$109$	−1.33687	−0.128049	−0.0640244	+	0.997948i	$0.520394\pi$
$110$	−27.3946	−2.61197
$111$	1.94322	0.184442
$112$	63.6914	6.01827
$113$	−2.02195	−0.190209	−0.0951044	−	0.995467i	$-0.530319\pi$
$113$	−2.02195	−0.190209	−0.0951044	+	0.995467i	$0.530319\pi$
$114$	−14.5958	−1.36702
$115$	−4.22472	−0.393957
$116$	29.7343	2.76076
$117$	6.42536	0.594024
$118$	−3.20193	−0.294762
$119$	−22.5126	−2.06373
$120$	−33.3218	−3.04185
$121$	−0.743368	−0.0675789
$122$	−2.10067	−0.190186
$123$	−8.32135	−0.750310
$124$	−54.9940	−4.93861
$125$	−2.23112	−0.199557
$126$	−9.43606	−0.840631
$127$	−11.3783	−1.00966	−0.504830	−	0.863219i	$-0.668445\pi$
$127$	−11.3783	−1.00966	−0.504830	+	0.863219i	$0.668445\pi$
$128$	−78.5394	−6.94197
$129$	7.92471	0.697732
$130$	−54.9616	−4.82045
$131$	−19.9280	−1.74112	−0.870560	−	0.492063i	$-0.836243\pi$
$131$	−19.9280	−1.74112	−0.870560	+	0.492063i	$0.836243\pi$
$132$	18.8810	1.64338
$133$	17.4436	1.51255
$134$	−18.0664	−1.56070
$135$	3.04419	0.262002
$136$	73.3808	6.29235
$137$	15.6869	1.34022	0.670110	−	0.742262i	$-0.266247\pi$
$137$	15.6869	1.34022	0.670110	+	0.742262i	$0.266247\pi$
$138$	3.89957	0.331953
$139$	9.20531	0.780785	0.390392	−	0.920649i	$-0.372339\pi$
$139$	9.20531	0.780785	0.390392	+	0.920649i	$0.372339\pi$
$140$	60.2691	5.09367
$141$	3.46968	0.292200
$142$	21.3602	1.79251
$143$	20.5778	1.72080
$144$	18.9662	1.58052
$145$	15.3535	1.27504
$146$	33.1894	2.74677
$147$	4.27717	0.352775
$148$	11.4563	0.941704
$149$	0.979608	0.0802527	0.0401263	−	0.999195i	$-0.487224\pi$
$149$	0.979608	0.0802527	0.0401263	+	0.999195i	$0.487224\pi$
$150$	−11.9901	−0.978987
$151$	7.47753	0.608512	0.304256	−	0.952590i	$-0.401592\pi$
$151$	7.47753	0.608512	0.304256	+	0.952590i	$0.401592\pi$
$152$	−56.8582	−4.61181
$153$	−6.70387	−0.541976
$154$	−30.2199	−2.43519
$155$	−28.3965	−2.28086
$156$	37.8809	3.03290
$157$	5.68385	0.453620	0.226810	−	0.973939i	$-0.427170\pi$
$157$	5.68385	0.453620	0.226810	+	0.973939i	$0.427170\pi$
$158$	46.9652	3.73635
$159$	0.587042	0.0465554
$160$	−95.5907	−7.55711
$161$	−4.66043	−0.367294
$162$	−2.80990	−0.220766
$163$	16.2555	1.27323	0.636613	−	0.771183i	$-0.280335\pi$
$163$	16.2555	1.27323	0.636613	+	0.771183i	$0.280335\pi$
$164$	−49.0587	−3.83084
$165$	9.74931	0.758983
$166$	−22.8464	−1.77323
$167$	14.5432	1.12538	0.562691	−	0.826667i	$-0.309766\pi$
$167$	14.5432	1.12538	0.562691	+	0.826667i	$0.309766\pi$
$168$	−36.7584	−2.83598
$169$	28.2852	2.17579
$170$	57.3440	4.39808
$171$	5.19441	0.397227
$172$	46.7204	3.56239
$173$	6.95597	0.528853	0.264426	−	0.964406i	$-0.414817\pi$
$173$	6.95597	0.528853	0.264426	+	0.964406i	$0.414817\pi$
$174$	−14.1718	−1.07436
$175$	14.3295	1.08321
$176$	60.7411	4.57853
$177$	1.13952	0.0856515
$178$	−24.6901	−1.85060
$179$	−12.2263	−0.913836	−0.456918	−	0.889509i	$-0.651047\pi$
$179$	−12.2263	−0.913836	−0.456918	+	0.889509i	$0.651047\pi$
$180$	17.9471	1.33770
$181$	20.6717	1.53651	0.768256	−	0.640142i	$-0.221125\pi$
$181$	20.6717	1.53651	0.768256	+	0.640142i	$0.221125\pi$
$182$	−60.6301	−4.49420
$183$	0.747596	0.0552639
$184$	15.1909	1.11989
$185$	5.91553	0.434919
$186$	26.2110	1.92188
$187$	−21.4698	−1.57003
$188$	20.4556	1.49188
$189$	3.35815	0.244269
$190$	−44.4323	−3.22346
$191$	−14.1794	−1.02598	−0.512992	−	0.858393i	$-0.671463\pi$
$191$	−14.1794	−1.02598	−0.512992	+	0.858393i	$0.671463\pi$
$192$	50.3013	3.63018
$193$	−0.765741	−0.0551192	−0.0275596	−	0.999620i	$-0.508774\pi$
$193$	−0.765741	−0.0551192	−0.0275596	+	0.999620i	$0.508774\pi$
$194$	15.8525	1.13814
$195$	19.5600	1.40072
$196$	25.2162	1.80116
$197$	18.5619	1.32248	0.661240	−	0.750174i	$-0.270030\pi$
$197$	18.5619	1.32248	0.661240	+	0.750174i	$0.270030\pi$
$198$	−8.99897	−0.639529
$199$	−8.00176	−0.567229	−0.283615	−	0.958938i	$-0.591534\pi$
$199$	−8.00176	−0.567229	−0.283615	+	0.958938i	$0.591534\pi$
$200$	−46.7077	−3.30274
$201$	6.42956	0.453506
$202$	−27.2855	−1.91980
$203$	16.9370	1.18874
$204$	−39.5228	−2.76715
$205$	−25.3318	−1.76925
$206$	34.8778	2.43005
$207$	−1.38780	−0.0964586
$208$	121.865	8.44979
$209$	16.6356	1.15071
$210$	−28.7252	−1.98222
$211$	0.888070	0.0611373	0.0305686	−	0.999533i	$-0.490268\pi$
$211$	0.888070	0.0611373	0.0305686	+	0.999533i	$0.490268\pi$
$212$	3.46092	0.237697
$213$	−7.60177	−0.520864
$214$	−38.1029	−2.60466
$215$	24.1243	1.64526
$216$	−10.9460	−0.744784
$217$	−31.3251	−2.12649
$218$	3.75647	0.254420
$219$	−11.8116	−0.798154
$220$	57.4774	3.87512
$221$	−43.0747	−2.89752
$222$	−5.46025	−0.366468
$223$	3.86891	0.259081	0.129541	−	0.991574i	$-0.458650\pi$
$223$	3.86891	0.259081	0.129541	+	0.991574i	$0.458650\pi$
$224$	−105.449	−7.04563
$225$	4.26709	0.284473
$226$	5.68147	0.377926
$227$	22.1461	1.46989	0.734944	−	0.678128i	$-0.237209\pi$
$227$	22.1461	1.46989	0.734944	+	0.678128i	$0.237209\pi$
$228$	30.6238	2.02811
$229$	−23.0646	−1.52415	−0.762075	−	0.647489i	$-0.775819\pi$
$229$	−23.0646	−1.52415	−0.762075	+	0.647489i	$0.775819\pi$
$230$	11.8710	0.782753
$231$	10.7548	0.707614
$232$	−55.2068	−3.62450
$233$	10.4477	0.684449	0.342224	−	0.939618i	$-0.388820\pi$
$233$	10.4477	0.684449	0.342224	+	0.939618i	$0.388820\pi$
$234$	−18.0546	−1.18027
$235$	10.5624	0.689013
$236$	6.71807	0.437309
$237$	−16.7142	−1.08570
$238$	63.2581	4.10041
$239$	−7.95972	−0.514871	−0.257436	−	0.966295i	$-0.582878\pi$
$239$	−7.95972	−0.514871	−0.257436	+	0.966295i	$0.582878\pi$
$240$	57.7367	3.72689
$241$	14.2075	0.915187	0.457593	−	0.889162i	$-0.348712\pi$
$241$	14.2075	0.915187	0.457593	+	0.889162i	$0.348712\pi$
$242$	2.08879	0.134272
$243$	1.00000	0.0641500
$244$	4.40747	0.282159
$245$	13.0205	0.831850
$246$	23.3821	1.49079
$247$	33.3759	2.12366
$248$	102.106	6.48371
$249$	8.13069	0.515261
$250$	6.26922	0.396500
$251$	−18.6693	−1.17840	−0.589198	−	0.807989i	$-0.700556\pi$
$251$	−18.6693	−1.17840	−0.589198	+	0.807989i	$0.700556\pi$
$252$	19.7981	1.24716
$253$	−4.44456	−0.279427
$254$	31.9718	2.00609
$255$	−20.4078	−1.27799
$256$	120.085	7.50533
$257$	−10.4419	−0.651345	−0.325673	−	0.945483i	$-0.605591\pi$
$257$	−10.4419	−0.651345	−0.325673	+	0.945483i	$0.605591\pi$
$258$	−22.2676	−1.38632
$259$	6.52563	0.405483
$260$	115.317	7.15163
$261$	5.04354	0.312187
$262$	55.9957	3.45943
$263$	−5.53127	−0.341073	−0.170537	−	0.985351i	$-0.554550\pi$
$263$	−5.53127	−0.341073	−0.170537	+	0.985351i	$0.554550\pi$
$264$	−35.0558	−2.15753
$265$	1.78707	0.109779
$266$	−49.0148	−3.00529
$267$	8.78685	0.537746
$268$	37.9057	2.31546
$269$	11.5422	0.703737	0.351869	−	0.936049i	$-0.385546\pi$
$269$	11.5422	0.703737	0.351869	+	0.936049i	$0.385546\pi$
$270$	−8.55386	−0.520572
$271$	22.0844	1.34153	0.670765	−	0.741670i	$-0.265966\pi$
$271$	22.0844	1.34153	0.670765	+	0.741670i	$0.265966\pi$
$272$	−127.147	−7.70942
$273$	21.5773	1.30592
$274$	−44.0785	−2.66288
$275$	13.6658	0.824077
$276$	−8.18180	−0.492487
$277$	3.78938	0.227682	0.113841	−	0.993499i	$-0.463685\pi$
$277$	3.78938	0.227682	0.113841	+	0.993499i	$0.463685\pi$
$278$	−25.8660	−1.55134
$279$	−9.32809	−0.558458
$280$	−111.900	−6.68728
$281$	1.91327	0.114136	0.0570682	−	0.998370i	$-0.481825\pi$
$281$	1.91327	0.114136	0.0570682	+	0.998370i	$0.481825\pi$
$282$	−9.74945	−0.580572
$283$	18.7545	1.11484	0.557420	−	0.830231i	$-0.311791\pi$
$283$	18.7545	1.11484	0.557420	+	0.830231i	$0.311791\pi$
$284$	−44.8164	−2.65937
$285$	15.8128	0.936668
$286$	−57.8216	−3.41906
$287$	−27.9443	−1.64950
$288$	−31.4010	−1.85032
$289$	27.9418	1.64364
$290$	−43.1417	−2.53337
$291$	−5.64165	−0.330719
$292$	−69.6356	−4.07512
$293$	−30.8106	−1.79997	−0.899986	−	0.435919i	$-0.856423\pi$
$293$	−30.8106	−1.79997	−0.899986	+	0.435919i	$0.856423\pi$
$294$	−12.0184	−0.700928
$295$	3.46891	0.201968
$296$	−21.2706	−1.23633
$297$	3.20260	0.185834
$298$	−2.75260	−0.159454
$299$	−8.91709	−0.515689
$300$	25.1567	1.45243
$301$	26.6124	1.53391
$302$	−21.0111	−1.20905
$303$	9.71049	0.557853
$304$	98.5183	5.65041
$305$	2.27582	0.130313
$306$	18.8372	1.07685
$307$	−14.0122	−0.799718	−0.399859	−	0.916577i	$-0.630941\pi$
$307$	−14.0122	−0.799718	−0.399859	+	0.916577i	$0.630941\pi$
$308$	63.4053	3.61285
$309$	−12.4125	−0.706122
$310$	79.7912	4.53183
$311$	−10.0144	−0.567864	−0.283932	−	0.958844i	$-0.591639\pi$
$311$	−10.0144	−0.567864	−0.283932	+	0.958844i	$0.591639\pi$
$312$	−70.3322	−3.98178
$313$	16.3140	0.922124	0.461062	−	0.887368i	$-0.347469\pi$
$313$	16.3140	0.922124	0.461062	+	0.887368i	$0.347469\pi$
$314$	−15.9710	−0.901297
$315$	10.2228	0.575992
$316$	−98.5390	−5.54325
$317$	10.8648	0.610226	0.305113	−	0.952316i	$-0.401306\pi$
$317$	10.8648	0.610226	0.305113	+	0.952316i	$0.401306\pi$
$318$	−1.64953	−0.0925009
$319$	16.1524	0.904362
$320$	153.127	8.56004
$321$	13.5602	0.756858
$322$	13.0953	0.729775
$323$	−34.8227	−1.93758
$324$	5.89553	0.327529
$325$	27.4176	1.52085
$326$	−45.6762	−2.52977
$327$	−1.33687	−0.0739290
$328$	91.0858	5.02937
$329$	11.6517	0.642380
$330$	−27.3946	−1.50802
$331$	10.3965	0.571441	0.285721	−	0.958313i	$-0.407767\pi$
$331$	10.3965	0.571441	0.285721	+	0.958313i	$0.407767\pi$
$332$	47.9347	2.63076
$333$	1.94322	0.106488
$334$	−40.8648	−2.23602
$335$	19.5728	1.06938
$336$	63.6914	3.47465
$337$	20.5785	1.12098	0.560490	−	0.828161i	$-0.310613\pi$
$337$	20.5785	1.12098	0.560490	+	0.828161i	$0.310613\pi$
$338$	−79.4786	−4.32306
$339$	−2.02195	−0.109817
$340$	−120.315	−6.52500
$341$	−29.8741	−1.61777
$342$	−14.5958	−0.789249
$343$	−9.14367	−0.493712
$344$	−86.7442	−4.67693
$345$	−4.22472	−0.227451
$346$	−19.5456	−1.05078
$347$	32.1402	1.72537	0.862687	−	0.505737i	$-0.168780\pi$
$347$	32.1402	1.72537	0.862687	+	0.505737i	$0.168780\pi$
$348$	29.7343	1.59393
$349$	−16.9573	−0.907705	−0.453852	−	0.891077i	$-0.649951\pi$
$349$	−16.9573	−0.907705	−0.453852	+	0.891077i	$0.649951\pi$
$350$	−40.2645	−2.15223
$351$	6.42536	0.342960
$352$	−100.565	−5.36012
$353$	−8.54370	−0.454735	−0.227368	−	0.973809i	$-0.573012\pi$
$353$	−8.54370	−0.454735	−0.227368	+	0.973809i	$0.573012\pi$
$354$	−3.20193	−0.170181
$355$	−23.1412	−1.22821
$356$	51.8031	2.74556
$357$	−22.5126	−1.19149
$358$	34.3546	1.81570
$359$	−6.18853	−0.326618	−0.163309	−	0.986575i	$-0.552217\pi$
$359$	−6.18853	−0.326618	−0.163309	+	0.986575i	$0.552217\pi$
$360$	−33.3218	−1.75621
$361$	7.98191	0.420101
$362$	−58.0853	−3.05289
$363$	−0.743368	−0.0390167
$364$	127.210	6.66760
$365$	−35.9567	−1.88206
$366$	−2.10067	−0.109804
$367$	2.79062	0.145669	0.0728346	−	0.997344i	$-0.476795\pi$
$367$	2.79062	0.145669	0.0728346	+	0.997344i	$0.476795\pi$
$368$	−26.3213	−1.37209
$369$	−8.32135	−0.433192
$370$	−16.6221	−0.864139
$371$	1.97137	0.102349
$372$	−54.9940	−2.85131
$373$	−18.6934	−0.967906	−0.483953	−	0.875094i	$-0.660799\pi$
$373$	−18.6934	−0.967906	−0.483953	+	0.875094i	$0.660799\pi$
$374$	60.3279	3.11948
$375$	−2.23112	−0.115214
$376$	−37.9793	−1.95863
$377$	32.4065	1.66902
$378$	−9.43606	−0.485339
$379$	−37.8175	−1.94255	−0.971276	−	0.237954i	$-0.923523\pi$
$379$	−37.8175	−1.94255	−0.971276	+	0.237954i	$0.923523\pi$
$380$	93.2247	4.78232
$381$	−11.3783	−0.582928
$382$	39.8426	2.03853
$383$	−24.5986	−1.25693	−0.628465	−	0.777838i	$-0.716316\pi$
$383$	−24.5986	−1.25693	−0.628465	+	0.777838i	$0.716316\pi$
$384$	−78.5394	−4.00795
$385$	32.7397	1.66857
$386$	2.15165	0.109516
$387$	7.92471	0.402836
$388$	−33.2605	−1.68855
$389$	5.32796	0.270138	0.135069	−	0.990836i	$-0.456874\pi$
$389$	5.32796	0.270138	0.135069	+	0.990836i	$0.456874\pi$
$390$	−54.9616	−2.78309
$391$	9.30361	0.470504
$392$	−46.8181	−2.36467
$393$	−19.9280	−1.00524
$394$	−52.1571	−2.62763
$395$	−50.8812	−2.56011
$396$	18.8810	0.948806
$397$	−24.8955	−1.24947	−0.624736	−	0.780836i	$-0.714793\pi$
$397$	−24.8955	−1.24947	−0.624736	+	0.780836i	$0.714793\pi$
$398$	22.4841	1.12703
$399$	17.4436	0.873273
$400$	80.9305	4.04652
$401$	−32.7752	−1.63671	−0.818357	−	0.574710i	$-0.805115\pi$
$401$	−32.7752	−1.63671	−0.818357	+	0.574710i	$0.805115\pi$
$402$	−18.0664	−0.901071
$403$	−59.9363	−2.98564
$404$	57.2484	2.84822
$405$	3.04419	0.151267
$406$	−47.5911	−2.36191
$407$	6.22336	0.308480
$408$	73.3808	3.63289
$409$	11.1653	0.552086	0.276043	−	0.961145i	$-0.410977\pi$
$409$	11.1653	0.552086	0.276043	+	0.961145i	$0.410977\pi$
$410$	71.1797	3.51531
$411$	15.6869	0.773777
$412$	−73.1782	−3.60523
$413$	3.82668	0.188298
$414$	3.89957	0.191653
$415$	24.7514	1.21500
$416$	−201.763	−9.89223
$417$	9.20531	0.450786
$418$	−46.7444	−2.28634
$419$	−27.6146	−1.34906	−0.674531	−	0.738247i	$-0.735654\pi$
$419$	−27.6146	−1.34906	−0.674531	+	0.738247i	$0.735654\pi$
$420$	60.2691	2.94083
$421$	−23.0100	−1.12144	−0.560720	−	0.828005i	$-0.689476\pi$
$421$	−23.0100	−1.12144	−0.560720	+	0.828005i	$0.689476\pi$
$422$	−2.49539	−0.121474
$423$	3.46968	0.168702
$424$	−6.42578	−0.312064
$425$	−28.6060	−1.38760
$426$	21.3602	1.03490
$427$	2.51054	0.121493
$428$	79.9447	3.86428
$429$	20.5778	0.993507
$430$	−67.7869	−3.26897
$431$	−16.5516	−0.797263	−0.398632	−	0.917111i	$-0.630515\pi$
$431$	−16.5516	−0.797263	−0.398632	+	0.917111i	$0.630515\pi$
$432$	18.9662	0.912512
$433$	−24.0720	−1.15683	−0.578414	−	0.815743i	$-0.696328\pi$
$433$	−24.0720	−1.15683	−0.578414	+	0.815743i	$0.696328\pi$
$434$	88.0204	4.22511
$435$	15.3535	0.736143
$436$	−7.88155	−0.377458
$437$	−7.20879	−0.344843
$438$	33.1894	1.58585
$439$	1.33516	0.0637236	0.0318618	−	0.999492i	$-0.489856\pi$
$439$	1.33516	0.0637236	0.0318618	+	0.999492i	$0.489856\pi$
$440$	−106.716	−5.08750
$441$	4.27717	0.203675
$442$	121.036	5.75708
$443$	39.9217	1.89674	0.948369	−	0.317169i	$-0.102732\pi$
$443$	39.9217	1.89674	0.948369	+	0.317169i	$0.102732\pi$
$444$	11.4563	0.543693
$445$	26.7488	1.26802
$446$	−10.8712	−0.514768
$447$	0.979608	0.0463339
$448$	168.919	7.98068
$449$	−7.11287	−0.335677	−0.167838	−	0.985815i	$-0.553679\pi$
$449$	−7.11287	−0.335677	−0.167838	+	0.985815i	$0.553679\pi$
$450$	−11.9901	−0.565218
$451$	−26.6499	−1.25490
$452$	−11.9205	−0.560691
$453$	7.47753	0.351325
$454$	−62.2283	−2.92052
$455$	65.6854	3.07938
$456$	−56.8582	−2.66263
$457$	−20.5783	−0.962610	−0.481305	−	0.876553i	$-0.659837\pi$
$457$	−20.5783	−0.962610	−0.481305	+	0.876553i	$0.659837\pi$
$458$	64.8091	3.02833
$459$	−6.70387	−0.312910
$460$	−24.9070	−1.16129
$461$	−1.67068	−0.0778113	−0.0389056	−	0.999243i	$-0.512387\pi$
$461$	−1.67068	−0.0778113	−0.0389056	+	0.999243i	$0.512387\pi$
$462$	−30.2199	−1.40596
$463$	−9.34083	−0.434105	−0.217053	−	0.976160i	$-0.569644\pi$
$463$	−9.34083	−0.434105	−0.217053	+	0.976160i	$0.569644\pi$
$464$	95.6568	4.44076
$465$	−28.3965	−1.31685
$466$	−29.3568	−1.35993
$467$	17.1994	0.795895	0.397947	−	0.917408i	$-0.369723\pi$
$467$	17.1994	0.795895	0.397947	+	0.917408i	$0.369723\pi$
$468$	37.8809	1.75104
$469$	21.5914	0.997000
$470$	−29.6792	−1.36900
$471$	5.68385	0.261898
$472$	−12.4732	−0.574127
$473$	25.3797	1.16696
$474$	46.9652	2.15718
$475$	22.1650	1.01700
$476$	−132.724	−6.08338
$477$	0.587042	0.0268788
$478$	22.3660	1.02300
$479$	19.4740	0.889788	0.444894	−	0.895583i	$-0.353241\pi$
$479$	19.4740	0.889788	0.444894	+	0.895583i	$0.353241\pi$
$480$	−95.5907	−4.36310
$481$	12.4859	0.569308
$482$	−39.9217	−1.81838
$483$	−4.66043	−0.212057
$484$	−4.38255	−0.199207
$485$	−17.1742	−0.779842
$486$	−2.80990	−0.127460
$487$	−30.3286	−1.37432	−0.687159	−	0.726507i	$-0.741143\pi$
$487$	−30.3286	−1.37432	−0.687159	+	0.726507i	$0.741143\pi$
$488$	−8.18321	−0.370437
$489$	16.2555	0.735098
$490$	−36.5863	−1.65280
$491$	18.2150	0.822031	0.411016	−	0.911628i	$-0.365174\pi$
$491$	18.2150	0.822031	0.411016	+	0.911628i	$0.365174\pi$
$492$	−49.0587	−2.21174
$493$	−33.8112	−1.52278
$494$	−93.7830	−4.21950
$495$	9.74931	0.438199
$496$	−176.918	−7.94387
$497$	−25.5279	−1.14508
$498$	−22.8464	−1.02377
$499$	−28.3566	−1.26942	−0.634708	−	0.772752i	$-0.718880\pi$
$499$	−28.3566	−1.26942	−0.634708	+	0.772752i	$0.718880\pi$
$500$	−13.1536	−0.588248
$501$	14.5432	0.649740
$502$	52.4588	2.34135
$503$	19.1039	0.851799	0.425900	−	0.904770i	$-0.359958\pi$
$503$	19.1039	0.851799	0.425900	+	0.904770i	$0.359958\pi$
$504$	−36.7584	−1.63735
$505$	29.5606	1.31543
$506$	12.4888	0.555193
$507$	28.2852	1.25619
$508$	−67.0810	−2.97624
$509$	29.0448	1.28739	0.643693	−	0.765284i	$-0.277401\pi$
$509$	29.0448	1.28739	0.643693	+	0.765284i	$0.277401\pi$
$510$	57.3440	2.53923
$511$	−39.6651	−1.75468
$512$	−180.349	−7.97036
$513$	5.19441	0.229339
$514$	29.3406	1.29416
$515$	−37.7860	−1.66505
$516$	46.7204	2.05675
$517$	11.1120	0.488705
$518$	−18.3364	−0.805653
$519$	6.95597	0.305333
$520$	−214.105	−9.38911
$521$	−4.67184	−0.204677	−0.102339	−	0.994750i	$-0.532632\pi$
$521$	−4.67184	−0.204677	−0.102339	+	0.994750i	$0.532632\pi$
$522$	−14.1718	−0.620284
$523$	−3.51047	−0.153502	−0.0767510	−	0.997050i	$-0.524455\pi$
$523$	−3.51047	−0.153502	−0.0767510	+	0.997050i	$0.524455\pi$
$524$	−117.486	−5.13241
$525$	14.3295	0.625392
$526$	15.5423	0.677677
$527$	62.5343	2.72404
$528$	60.7411	2.64342
$529$	−21.0740	−0.916262
$530$	−5.02147	−0.218119
$531$	1.13952	0.0494509
$532$	102.839	4.45865
$533$	−53.4676	−2.31594
$534$	−24.6901	−1.06845
$535$	41.2799	1.78469
$536$	−70.3783	−3.03988
$537$	−12.2263	−0.527603
$538$	−32.4323	−1.39825
$539$	13.6981	0.590017
$540$	17.9471	0.772321
$541$	−11.5446	−0.496340	−0.248170	−	0.968716i	$-0.579829\pi$
$541$	−11.5446	−0.496340	−0.248170	+	0.968716i	$0.579829\pi$
$542$	−62.0549	−2.66548
$543$	20.6717	0.887106
$544$	210.508	9.02547
$545$	−4.06968	−0.174326
$546$	−60.6301	−2.59473
$547$	−18.5907	−0.794883	−0.397442	−	0.917628i	$-0.630102\pi$
$547$	−18.5907	−0.794883	−0.397442	+	0.917628i	$0.630102\pi$
$548$	92.4825	3.95065
$549$	0.747596	0.0319066
$550$	−38.3994	−1.63736
$551$	26.1982	1.11608
$552$	15.1909	0.646567
$553$	−56.1288	−2.38684
$554$	−10.6478	−0.452380
$555$	5.91553	0.251100
$556$	54.2702	2.30157
$557$	−23.1557	−0.981139	−0.490569	−	0.871402i	$-0.663211\pi$
$557$	−23.1557	−0.981139	−0.490569	+	0.871402i	$0.663211\pi$
$558$	26.2110	1.10960
$559$	50.9191	2.15365
$560$	193.889	8.19329
$561$	−21.4698	−0.906455
$562$	−5.37611	−0.226777
$563$	29.8727	1.25899	0.629493	−	0.777006i	$-0.283263\pi$
$563$	29.8727	1.25899	0.629493	+	0.777006i	$0.283263\pi$
$564$	20.4556	0.861337
$565$	−6.15519	−0.258951
$566$	−52.6982	−2.21507
$567$	3.35815	0.141029
$568$	83.2093	3.49138
$569$	19.2278	0.806073	0.403037	−	0.915184i	$-0.367955\pi$
$569$	19.2278	0.806073	0.403037	+	0.915184i	$0.367955\pi$
$570$	−44.4323	−1.86106
$571$	15.3237	0.641278	0.320639	−	0.947201i	$-0.396102\pi$
$571$	15.3237	0.641278	0.320639	+	0.947201i	$0.396102\pi$
$572$	121.317	5.07253
$573$	−14.1794	−0.592352
$574$	78.5207	3.27739
$575$	−5.92186	−0.246958
$576$	50.3013	2.09589
$577$	4.30161	0.179078	0.0895391	−	0.995983i	$-0.471461\pi$
$577$	4.30161	0.179078	0.0895391	+	0.995983i	$0.471461\pi$
$578$	−78.5138	−3.26574
$579$	−0.765741	−0.0318231
$580$	90.5169	3.75851
$581$	27.3041	1.13276
$582$	15.8525	0.657105
$583$	1.88006	0.0778640
$584$	129.290	5.35007
$585$	19.5600	0.808707
$586$	86.5745	3.57636
$587$	−26.0410	−1.07483	−0.537413	−	0.843319i	$-0.680598\pi$
$587$	−26.0410	−1.07483	−0.537413	+	0.843319i	$0.680598\pi$
$588$	25.2162	1.03990
$589$	−48.4539	−1.99651
$590$	−9.74729	−0.401290
$591$	18.5619	0.763535
$592$	36.8555	1.51475
$593$	−38.1855	−1.56809	−0.784044	−	0.620705i	$-0.786847\pi$
$593$	−38.1855	−1.56809	−0.784044	+	0.620705i	$0.786847\pi$
$594$	−8.99897	−0.369232
$595$	−68.5326	−2.80956
$596$	5.77531	0.236566
$597$	−8.00176	−0.327490
$598$	25.0561	1.02462
$599$	−28.8538	−1.17893	−0.589467	−	0.807793i	$-0.700662\pi$
$599$	−28.8538	−1.17893	−0.589467	+	0.807793i	$0.700662\pi$
$600$	−46.7077	−1.90684
$601$	31.6629	1.29156	0.645778	−	0.763525i	$-0.276533\pi$
$601$	31.6629	1.29156	0.645778	+	0.763525i	$0.276533\pi$
$602$	−74.7780	−3.04773
$603$	6.42956	0.261832
$604$	44.0840	1.79375
$605$	−2.26295	−0.0920022
$606$	−27.2855	−1.10840
$607$	−41.0335	−1.66550	−0.832750	−	0.553649i	$-0.813235\pi$
$607$	−41.0335	−1.66550	−0.832750	+	0.553649i	$0.813235\pi$
$608$	−163.110	−6.61498
$609$	16.9370	0.686320
$610$	−6.39483	−0.258919
$611$	22.2939	0.901916
$612$	−39.5228	−1.59762
$613$	41.0538	1.65815	0.829073	−	0.559140i	$-0.188868\pi$
$613$	41.0538	1.65815	0.829073	+	0.559140i	$0.188868\pi$
$614$	39.3728	1.58896
$615$	−25.3318	−1.02147
$616$	−117.723	−4.74318
$617$	−36.6857	−1.47691	−0.738456	−	0.674302i	$-0.764445\pi$
$617$	−36.6857	−1.47691	−0.738456	+	0.674302i	$0.764445\pi$
$618$	34.8778	1.40299
$619$	26.0404	1.04665	0.523325	−	0.852133i	$-0.324691\pi$
$619$	26.0404	1.04665	0.523325	+	0.852133i	$0.324691\pi$
$620$	−167.412	−6.72343
$621$	−1.38780	−0.0556904
$622$	28.1394	1.12829
$623$	29.5075	1.18219
$624$	121.865	4.87849
$625$	−28.1274	−1.12510
$626$	−45.8408	−1.83217
$627$	16.6356	0.664362
$628$	33.5093	1.33717
$629$	−13.0271	−0.519425
$630$	−28.7252	−1.14444
$631$	22.6266	0.900750	0.450375	−	0.892839i	$-0.351290\pi$
$631$	22.6266	0.900750	0.450375	+	0.892839i	$0.351290\pi$
$632$	182.954	7.27753
$633$	0.888070	0.0352976
$634$	−30.5289	−1.21246
$635$	−34.6377	−1.37455
$636$	3.46092	0.137234
$637$	27.4823	1.08889
$638$	−45.3867	−1.79688
$639$	−7.60177	−0.300721
$640$	−239.089	−9.45082
$641$	−11.9147	−0.470603	−0.235301	−	0.971922i	$-0.575608\pi$
$641$	−11.9147	−0.470603	−0.235301	+	0.971922i	$0.575608\pi$
$642$	−38.1029	−1.50380
$643$	18.9926	0.748994	0.374497	−	0.927228i	$-0.377815\pi$
$643$	18.9926	0.748994	0.374497	+	0.927228i	$0.377815\pi$
$644$	−27.4757	−1.08269
$645$	24.1243	0.949894
$646$	97.8481	3.84978
$647$	6.29853	0.247621	0.123810	−	0.992306i	$-0.460489\pi$
$647$	6.29853	0.247621	0.123810	+	0.992306i	$0.460489\pi$
$648$	−10.9460	−0.430001
$649$	3.64942	0.143252
$650$	−77.0406	−3.02178
$651$	−31.3251	−1.22773
$652$	95.8346	3.75317
$653$	−28.7468	−1.12495	−0.562476	−	0.826814i	$-0.690151\pi$
$653$	−28.7468	−1.12495	−0.562476	+	0.826814i	$0.690151\pi$
$654$	3.75647	0.146889
$655$	−60.6647	−2.37036
$656$	−157.824	−6.16201
$657$	−11.8116	−0.460814
$658$	−32.7401	−1.27634
$659$	−34.5340	−1.34525	−0.672627	−	0.739982i	$-0.734834\pi$
$659$	−34.5340	−1.34525	−0.672627	+	0.739982i	$0.734834\pi$
$660$	57.4774	2.23730
$661$	−33.1508	−1.28942	−0.644709	−	0.764428i	$-0.723021\pi$
$661$	−33.1508	−1.28942	−0.644709	+	0.764428i	$0.723021\pi$
$662$	−29.2130	−1.13540
$663$	−43.0747	−1.67288
$664$	−88.9988	−3.45382
$665$	53.1017	2.05919
$666$	−5.46025	−0.211581
$667$	−6.99941	−0.271018
$668$	85.7396	3.31736
$669$	3.86891	0.149581
$670$	−54.9976	−2.12474
$671$	2.39425	0.0924289
$672$	−105.449	−4.06780
$673$	−25.6144	−0.987362	−0.493681	−	0.869643i	$-0.664349\pi$
$673$	−25.6144	−0.987362	−0.493681	+	0.869643i	$0.664349\pi$
$674$	−57.8234	−2.22727
$675$	4.26709	0.164240
$676$	166.756	6.41370
$677$	14.9934	0.576242	0.288121	−	0.957594i	$-0.406969\pi$
$677$	14.9934	0.576242	0.288121	+	0.957594i	$0.406969\pi$
$678$	5.68147	0.218195
$679$	−18.9455	−0.727061
$680$	223.385	8.56643
$681$	22.1461	0.848640
$682$	83.9432	3.21435
$683$	−30.1693	−1.15440	−0.577199	−	0.816604i	$-0.695854\pi$
$683$	−30.1693	−1.15440	−0.577199	+	0.816604i	$0.695854\pi$
$684$	30.6238	1.17093
$685$	47.7538	1.82458
$686$	25.6928	0.980955
$687$	−23.0646	−0.879969
$688$	150.302	5.73020
$689$	3.77195	0.143700
$690$	11.8710	0.451922
$691$	−13.9364	−0.530166	−0.265083	−	0.964226i	$-0.585399\pi$
$691$	−13.9364	−0.530166	−0.265083	+	0.964226i	$0.585399\pi$
$692$	41.0092	1.55893
$693$	10.7548	0.408541
$694$	−90.3106	−3.42814
$695$	28.0227	1.06296
$696$	−55.2068	−2.09261
$697$	55.7852	2.11302
$698$	47.6484	1.80352
$699$	10.4477	0.395167
$700$	84.4801	3.19305
$701$	14.7241	0.556120	0.278060	−	0.960564i	$-0.410309\pi$
$701$	14.7241	0.556120	0.278060	+	0.960564i	$0.410309\pi$
$702$	−18.0546	−0.681427
$703$	10.0939	0.380698
$704$	161.095	6.07149
$705$	10.5624	0.397802
$706$	24.0069	0.903513
$707$	32.6093	1.22640
$708$	6.71807	0.252481
$709$	−29.7409	−1.11694	−0.558471	−	0.829524i	$-0.688612\pi$
$709$	−29.7409	−1.11694	−0.558471	+	0.829524i	$0.688612\pi$
$710$	65.0245	2.44033
$711$	−16.7142	−0.626831
$712$	−96.1812	−3.60454
$713$	12.9455	0.484813
$714$	63.2581	2.36737
$715$	62.6428	2.34271
$716$	−72.0804	−2.69377
$717$	−7.95972	−0.297261
$718$	17.3891	0.648957
$719$	−31.7025	−1.18230	−0.591152	−	0.806560i	$-0.701327\pi$
$719$	−31.7025	−1.18230	−0.591152	+	0.806560i	$0.701327\pi$
$720$	57.7367	2.15172
$721$	−41.6830	−1.55236
$722$	−22.4284	−0.834697
$723$	14.2075	0.528383
$724$	121.870	4.52928
$725$	21.5212	0.799279
$726$	2.08879	0.0775223
$727$	20.0741	0.744509	0.372254	−	0.928131i	$-0.378585\pi$
$727$	20.0741	0.744509	0.372254	+	0.928131i	$0.378585\pi$
$728$	−236.186	−8.75364
$729$	1.00000	0.0370370
$730$	101.035	3.73946
$731$	−53.1262	−1.96494
$732$	4.40747	0.162905
$733$	−43.9540	−1.62348	−0.811739	−	0.584021i	$-0.801479\pi$
$733$	−43.9540	−1.62348	−0.811739	+	0.584021i	$0.801479\pi$
$734$	−7.84136	−0.289430
$735$	13.0205	0.480269
$736$	43.5783	1.60632
$737$	20.5913	0.758490
$738$	23.3821	0.860708
$739$	37.9757	1.39696	0.698479	−	0.715631i	$-0.253861\pi$
$739$	37.9757	1.39696	0.698479	+	0.715631i	$0.253861\pi$
$740$	34.8752	1.28204
$741$	33.3759	1.22610
$742$	−5.53936	−0.203356
$743$	4.43263	0.162618	0.0813088	−	0.996689i	$-0.474090\pi$
$743$	4.43263	0.162618	0.0813088	+	0.996689i	$0.474090\pi$
$744$	102.106	3.74337
$745$	2.98211	0.109256
$746$	52.5265	1.92313
$747$	8.13069	0.297486
$748$	−126.576	−4.62807
$749$	45.5373	1.66390
$750$	6.26922	0.228919
$751$	23.4537	0.855839	0.427919	−	0.903817i	$-0.359247\pi$
$751$	23.4537	0.855839	0.427919	+	0.903817i	$0.359247\pi$
$752$	65.8067	2.39972
$753$	−18.6693	−0.680347
$754$	−91.0591	−3.31618
$755$	22.7630	0.828431
$756$	19.7981	0.720049
$757$	35.9715	1.30741	0.653703	−	0.756751i	$-0.273215\pi$
$757$	35.9715	1.30741	0.653703	+	0.756751i	$0.273215\pi$
$758$	106.263	3.85965
$759$	−4.44456	−0.161327
$760$	−173.087	−6.27853
$761$	−20.6344	−0.747998	−0.373999	−	0.927429i	$-0.622014\pi$
$761$	−20.6344	−0.747998	−0.373999	+	0.927429i	$0.622014\pi$
$762$	31.9718	1.15822
$763$	−4.48941	−0.162527
$764$	−83.5950	−3.02436
$765$	−20.4078	−0.737847
$766$	69.1195	2.49739
$767$	7.32182	0.264376
$768$	120.085	4.33320
$769$	47.5189	1.71358	0.856788	−	0.515669i	$-0.172457\pi$
$769$	47.5189	1.71358	0.856788	+	0.515669i	$0.172457\pi$
$770$	−91.9951	−3.31527
$771$	−10.4419	−0.376054
$772$	−4.51445	−0.162478
$773$	8.41211	0.302562	0.151281	−	0.988491i	$-0.451660\pi$
$773$	8.41211	0.302562	0.151281	+	0.988491i	$0.451660\pi$
$774$	−22.2676	−0.800393
$775$	−39.8038	−1.42979
$776$	61.7537	2.21683
$777$	6.52563	0.234106
$778$	−14.9710	−0.536737
$779$	−43.2245	−1.54868
$780$	115.317	4.12900
$781$	−24.3454	−0.871147
$782$	−26.1422	−0.934843
$783$	5.04354	0.180241
$784$	81.1217	2.89720
$785$	17.3027	0.617560
$786$	55.9957	1.99730
$787$	−0.188091	−0.00670471	−0.00335236	−	0.999994i	$-0.501067\pi$
$787$	−0.188091	−0.00670471	−0.00335236	+	0.999994i	$0.501067\pi$
$788$	109.432	3.89836
$789$	−5.53127	−0.196919
$790$	142.971	5.08668
$791$	−6.79000	−0.241425
$792$	−35.0558	−1.24565
$793$	4.80357	0.170580
$794$	69.9540	2.48257
$795$	1.78707	0.0633807
$796$	−47.1746	−1.67206
$797$	27.4696	0.973024	0.486512	−	0.873674i	$-0.338269\pi$
$797$	27.4696	0.973024	0.486512	+	0.873674i	$0.338269\pi$
$798$	−49.0148	−1.73510
$799$	−23.2603	−0.822890
$800$	−133.991	−4.73730
$801$	8.78685	0.310468
$802$	92.0950	3.25199
$803$	−37.8278	−1.33491
$804$	37.9057	1.33683
$805$	−14.1872	−0.500034
$806$	168.415	5.93216
$807$	11.5422	0.406303
$808$	−106.291	−3.73932
$809$	21.4368	0.753678	0.376839	−	0.926279i	$-0.377011\pi$
$809$	21.4368	0.753678	0.376839	+	0.926279i	$0.377011\pi$
$810$	−8.55386	−0.300552
$811$	−49.4912	−1.73787	−0.868936	−	0.494925i	$-0.835196\pi$
$811$	−49.4912	−1.73787	−0.868936	+	0.494925i	$0.835196\pi$
$812$	99.8523	3.50413
$813$	22.0844	0.774533
$814$	−17.4870	−0.612919
$815$	49.4847	1.73337
$816$	−127.147	−4.45103
$817$	41.1642	1.44015
$818$	−31.3732	−1.09694
$819$	21.5773	0.753972
$820$	−149.344	−5.21532
$821$	−9.86523	−0.344299	−0.172149	−	0.985071i	$-0.555071\pi$
$821$	−9.86523	−0.344299	−0.172149	+	0.985071i	$0.555071\pi$
$822$	−44.0785	−1.53742
$823$	−34.0689	−1.18757	−0.593783	−	0.804625i	$-0.702366\pi$
$823$	−34.0689	−1.18757	−0.593783	+	0.804625i	$0.702366\pi$
$824$	135.868	4.73317
$825$	13.6658	0.475781
$826$	−10.7526	−0.374130
$827$	15.3046	0.532192	0.266096	−	0.963947i	$-0.414266\pi$
$827$	15.3046	0.532192	0.266096	+	0.963947i	$0.414266\pi$
$828$	−8.18180	−0.284337
$829$	45.1962	1.56973	0.784864	−	0.619668i	$-0.212733\pi$
$829$	45.1962	1.56973	0.784864	+	0.619668i	$0.212733\pi$
$830$	−69.5488	−2.41407
$831$	3.78938	0.131452
$832$	323.204	11.2051
$833$	−28.6736	−0.993481
$834$	−25.8660	−0.895666
$835$	44.2721	1.53210
$836$	98.0757	3.39202
$837$	−9.32809	−0.322426
$838$	77.5942	2.68045
$839$	−22.4717	−0.775808	−0.387904	−	0.921700i	$-0.626801\pi$
$839$	−22.4717	−0.775808	−0.387904	+	0.921700i	$0.626801\pi$
$840$	−111.900	−3.86091
$841$	−3.56271	−0.122852
$842$	64.6559	2.22819
$843$	1.91327	0.0658967
$844$	5.23564	0.180218
$845$	86.1055	2.96212
$846$	−9.74945	−0.335193
$847$	−2.49634	−0.0857753
$848$	11.1340	0.382341
$849$	18.7545	0.643653
$850$	80.3800	2.75701
$851$	−2.69680	−0.0924451
$852$	−44.8164	−1.53539
$853$	12.2200	0.418406	0.209203	−	0.977872i	$-0.432913\pi$
$853$	12.2200	0.418406	0.209203	+	0.977872i	$0.432913\pi$
$854$	−7.05436	−0.241395
$855$	15.8128	0.540785
$856$	−148.431	−5.07326
$857$	21.7194	0.741921	0.370961	−	0.928649i	$-0.379028\pi$
$857$	21.7194	0.741921	0.370961	+	0.928649i	$0.379028\pi$
$858$	−57.8216	−1.97400
$859$	−25.3645	−0.865425	−0.432712	−	0.901532i	$-0.642443\pi$
$859$	−25.3645	−0.865425	−0.432712	+	0.901532i	$0.642443\pi$
$860$	142.226	4.84985
$861$	−27.9443	−0.952340
$862$	46.5084	1.58408
$863$	51.8460	1.76486	0.882430	−	0.470445i	$-0.155906\pi$
$863$	51.8460	1.76486	0.882430	+	0.470445i	$0.155906\pi$
$864$	−31.4010	−1.06828
$865$	21.1753	0.719982
$866$	67.6400	2.29850
$867$	27.9418	0.948955
$868$	−184.678	−6.26838
$869$	−53.5288	−1.81584
$870$	−43.1417	−1.46264
$871$	41.3122	1.39981
$872$	14.6334	0.495550
$873$	−5.64165	−0.190941
$874$	20.2560	0.685169
$875$	−7.49243	−0.253290
$876$	−69.6356	−2.35277
$877$	10.2240	0.345241	0.172621	−	0.984988i	$-0.444777\pi$
$877$	10.2240	0.345241	0.172621	+	0.984988i	$0.444777\pi$
$878$	−3.75166	−0.126612
$879$	−30.8106	−1.03921
$880$	184.907	6.23323
$881$	18.0377	0.607704	0.303852	−	0.952719i	$-0.401727\pi$
$881$	18.0377	0.607704	0.303852	+	0.952719i	$0.401727\pi$
$882$	−12.0184	−0.404681
$883$	40.5288	1.36390	0.681951	−	0.731398i	$-0.261132\pi$
$883$	40.5288	1.36390	0.681951	+	0.731398i	$0.261132\pi$
$884$	−253.948	−8.54121
$885$	3.46891	0.116606
$886$	−112.176	−3.76863
$887$	−22.0297	−0.739685	−0.369843	−	0.929094i	$-0.620588\pi$
$887$	−22.0297	−0.739685	−0.369843	+	0.929094i	$0.620588\pi$
$888$	−21.2706	−0.713794
$889$	−38.2100	−1.28152
$890$	−75.1615	−2.51942
$891$	3.20260	0.107291
$892$	22.8093	0.763711
$893$	18.0230	0.603115
$894$	−2.75260	−0.0920607
$895$	−37.2191	−1.24410
$896$	−263.747	−8.81118
$897$	−8.91709	−0.297733
$898$	19.9864	0.666956
$899$	−47.0466	−1.56909
$900$	25.1567	0.838558
$901$	−3.93545	−0.131109
$902$	74.8836	2.49335
$903$	26.6124	0.885604
$904$	22.1323	0.736110
$905$	62.9285	2.09181
$906$	−21.0111	−0.698047
$907$	0.533840	0.0177259	0.00886293	−	0.999961i	$-0.497179\pi$
$907$	0.533840	0.0177259	0.00886293	+	0.999961i	$0.497179\pi$
$908$	130.563	4.33288
$909$	9.71049	0.322076
$910$	−184.569	−6.11841
$911$	19.1447	0.634293	0.317146	−	0.948377i	$-0.397275\pi$
$911$	19.1447	0.634293	0.317146	+	0.948377i	$0.397275\pi$
$912$	98.5183	3.26227
$913$	26.0393	0.861776
$914$	57.8228	1.91261
$915$	2.27582	0.0752364
$916$	−135.978	−4.49284
$917$	−66.9213	−2.20994
$918$	18.8372	0.621720
$919$	−35.0232	−1.15531	−0.577654	−	0.816282i	$-0.696032\pi$
$919$	−35.0232	−1.15531	−0.577654	+	0.816282i	$0.696032\pi$
$920$	46.2439	1.52462
$921$	−14.0122	−0.461717
$922$	4.69444	0.154603
$923$	−48.8441	−1.60772
$924$	63.4053	2.08588
$925$	8.29190	0.272636
$926$	26.2468	0.862523
$927$	−12.4125	−0.407680
$928$	−158.372	−5.19883
$929$	−58.4514	−1.91773	−0.958864	−	0.283864i	$-0.908383\pi$
$929$	−58.4514	−1.91773	−0.958864	+	0.283864i	$0.908383\pi$
$930$	79.7912	2.61646
$931$	22.2174	0.728145
$932$	61.5944	2.01759
$933$	−10.0144	−0.327857
$934$	−48.3287	−1.58136
$935$	−65.3581	−2.13744
$936$	−70.3322	−2.29888
$937$	0.192396	0.00628532	0.00314266	−	0.999995i	$-0.499000\pi$
$937$	0.192396	0.00628532	0.00314266	+	0.999995i	$0.499000\pi$
$938$	−60.6697	−1.98094
$939$	16.3140	0.532389
$940$	62.2708	2.03105
$941$	−37.0622	−1.20819	−0.604097	−	0.796911i	$-0.706466\pi$
$941$	−37.0622	−1.20819	−0.604097	+	0.796911i	$0.706466\pi$
$942$	−15.9710	−0.520364
$943$	11.5483	0.376066
$944$	21.6124	0.703422
$945$	10.2228	0.332549
$946$	−71.3143	−2.31863
$947$	48.2761	1.56876	0.784381	−	0.620279i	$-0.212981\pi$
$947$	48.2761	1.56876	0.784381	+	0.620279i	$0.212981\pi$
$948$	−98.5390	−3.20040
$949$	−75.8937	−2.46361
$950$	−62.2815	−2.02068
$951$	10.8648	0.352314
$952$	246.424	7.98664
$953$	−30.4525	−0.986452	−0.493226	−	0.869901i	$-0.664182\pi$
$953$	−30.4525	−0.986452	−0.493226	+	0.869901i	$0.664182\pi$
$954$	−1.64953	−0.0534054
$955$	−43.1647	−1.39678
$956$	−46.9267	−1.51772
$957$	16.1524	0.522134
$958$	−54.7198	−1.76792
$959$	52.6789	1.70109
$960$	153.127	4.94214
$961$	56.0132	1.80688
$962$	−35.0841	−1.13116
$963$	13.5602	0.436972
$964$	83.7608	2.69776
$965$	−2.33106	−0.0750395
$966$	13.0953	0.421336
$967$	−45.3354	−1.45789	−0.728944	−	0.684573i	$-0.759988\pi$
$967$	−45.3354	−1.45789	−0.728944	+	0.684573i	$0.759988\pi$
$968$	8.13694	0.261531
$969$	−34.8227	−1.11866
$970$	48.2579	1.54947
$971$	−1.99811	−0.0641225	−0.0320613	−	0.999486i	$-0.510207\pi$
$971$	−1.99811	−0.0641225	−0.0320613	+	0.999486i	$0.510207\pi$
$972$	5.89553	0.189099
$973$	30.9128	0.991020
$974$	85.2202	2.73063
$975$	27.4176	0.878065
$976$	14.1791	0.453860
$977$	28.9072	0.924824	0.462412	−	0.886665i	$-0.346984\pi$
$977$	28.9072	0.924824	0.462412	+	0.886665i	$0.346984\pi$
$978$	−45.6762	−1.46056
$979$	28.1407	0.899382
$980$	76.7628	2.45210
$981$	−1.33687	−0.0426830
$982$	−51.1823	−1.63329
$983$	40.6034	1.29505	0.647523	−	0.762046i	$-0.275805\pi$
$983$	40.6034	1.29505	0.647523	+	0.762046i	$0.275805\pi$
$984$	91.0858	2.90371
$985$	56.5059	1.80043
$986$	95.0061	3.02561
$987$	11.6517	0.370878
$988$	196.769	6.26005
$989$	−10.9979	−0.349713
$990$	−27.3946	−0.870657
$991$	−6.03170	−0.191603	−0.0958017	−	0.995400i	$-0.530541\pi$
$991$	−6.03170	−0.191603	−0.0958017	+	0.995400i	$0.530541\pi$
$992$	292.911	9.29995
$993$	10.3965	0.329922
$994$	71.7307	2.27516
$995$	−24.3589	−0.772228
$996$	47.9347	1.51887
$997$	−8.20945	−0.259996	−0.129998	−	0.991514i	$-0.541497\pi$
$997$	−8.20945	−0.259996	−0.129998	+	0.991514i	$0.541497\pi$
$998$	79.6792	2.52220
$999$	1.94322	0.0614808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.1	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.1	✓	129	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80990 q^{2} +1.00000 q^{3} +5.89553 q^{4} +3.04419 q^{5} -2.80990 q^{6} +3.35815 q^{7} -10.9460 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.80990 q^{2} +1.00000 q^{3} +5.89553 q^{4} +3.04419 q^{5} -2.80990 q^{6} +3.35815 q^{7} -10.9460 q^{8} +1.00000 q^{9} -8.55386 q^{10} +3.20260 q^{11} +5.89553 q^{12} +6.42536 q^{13} -9.43606 q^{14} +3.04419 q^{15} +18.9662 q^{16} -6.70387 q^{17} -2.80990 q^{18} +5.19441 q^{19} +17.9471 q^{20} +3.35815 q^{21} -8.99897 q^{22} -1.38780 q^{23} -10.9460 q^{24} +4.26709 q^{25} -18.0546 q^{26} +1.00000 q^{27} +19.7981 q^{28} +5.04354 q^{29} -8.55386 q^{30} -9.32809 q^{31} -31.4010 q^{32} +3.20260 q^{33} +18.8372 q^{34} +10.2228 q^{35} +5.89553 q^{36} +1.94322 q^{37} -14.5958 q^{38} +6.42536 q^{39} -33.3218 q^{40} -8.32135 q^{41} -9.43606 q^{42} +7.92471 q^{43} +18.8810 q^{44} +3.04419 q^{45} +3.89957 q^{46} +3.46968 q^{47} +18.9662 q^{48} +4.27717 q^{49} -11.9901 q^{50} -6.70387 q^{51} +37.8809 q^{52} +0.587042 q^{53} -2.80990 q^{54} +9.74931 q^{55} -36.7584 q^{56} +5.19441 q^{57} -14.1718 q^{58} +1.13952 q^{59} +17.9471 q^{60} +0.747596 q^{61} +26.2110 q^{62} +3.35815 q^{63} +50.3013 q^{64} +19.5600 q^{65} -8.99897 q^{66} +6.42956 q^{67} -39.5228 q^{68} -1.38780 q^{69} -28.7252 q^{70} -7.60177 q^{71} -10.9460 q^{72} -11.8116 q^{73} -5.46025 q^{74} +4.26709 q^{75} +30.6238 q^{76} +10.7548 q^{77} -18.0546 q^{78} -16.7142 q^{79} +57.7367 q^{80} +1.00000 q^{81} +23.3821 q^{82} +8.13069 q^{83} +19.7981 q^{84} -20.4078 q^{85} -22.2676 q^{86} +5.04354 q^{87} -35.0558 q^{88} +8.78685 q^{89} -8.55386 q^{90} +21.5773 q^{91} -8.18180 q^{92} -9.32809 q^{93} -9.74945 q^{94} +15.8128 q^{95} -31.4010 q^{96} -5.64165 q^{97} -12.0184 q^{98} +3.20260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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